Elliptic curve isogeny class with LMFDB label 485100.cm (Cremona label 485100cm)

• Label: 485100.cm
• Number of curves: $2$
• Conductor: $485100$
• CM: no
• Rank: $1$

Elliptic curves in class 485100.cm

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
485100.cm1	485100cm2	\([0, 0, 0, -812175, -241386250]\)	\(4662947952/717409\)	\(9115464755628000000\)	\([2]\)	\(7372800\)	\(2.3616\)	\(\Gamma_0(N)\)-optimal^*
485100.cm2	485100cm1	\([0, 0, 0, 88200, -20794375]\)	\(95551488/290521\)	\(-230711659620750000\)	\([2]\)	\(3686400\)	\(2.0150\)	\(\Gamma_0(N)\)-optimal^*

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 485100.cm1.

Rank

The elliptic curves in class 485100.cm have rank \(1\).

Complex multiplication

The elliptic curves in class 485100.cm do not have complex multiplication.

Modular form 485100.2.a.cm

Isogeny matrix

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.